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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 171, Number 1, Pages 26–32
DOI: https://doi.org/10.4213/tmf6912 (Mi tmf6912) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Bi-Hamiltonian ordinary differential equations with matrix variables

A. V. Odesskiia, V. N. Rubtsovbc, V. V. Sokolovd

a Brock University, St. Catharines, Canada
b Institute for Theoretical and Experimental Physics, Moscow, Russia
c LAREMA, CNRS, Université d'Angers, Angers, France
d Landau Institute for Theoretical Physics, RAS, Moscow, Russia
Full-text PDF (371 kB) Citations (15)
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DOI: https://doi.org/10.4213/tmf6912
Abstract: We consider a special class of Poisson brackets related to systems of ordinary differential equations with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets, and find the corresponding hierarchy of integrable models, which generalizes the two-component Manakov matrix system to the case of an arbitrary number of matrices.
Keywords: integrable ordinary differential equation with matrix unknowns, bi-Hamiltonian formalism, Manakov model.
Received: 07.05.2011
English version:
Theoretical and Mathematical Physics, 2012, Volume 171, Issue 1, Pages 442–447
DOI: https://doi.org/10.1007/s11232-012-0043-4
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Odesskii, V. N. Rubtsov, V. V. Sokolov, “Bi-Hamiltonian ordinary differential equations with matrix variables”, TMF, 171:1 (2012), 26–32; Theoret. and Math. Phys., 171:1 (2012), 442–447
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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